EXTENSÃO DE PROGRAMA GRÁFICO PARA ANÁLISE DE VIBRAÇÕES DE MODELOS ESTRUTURAIS RETICULADOS

Resumo

This paper aims to present a user-friendly graphical tool for the dynamic analysis of
reticulated structural models, such as trusses, frames and grillages, implemented entirely on Matlab®.
The code was written as an addition to the LESM (Linear Elements Structure Model) program, an
open source structural analysis software developed in Tecgraf/PUC-Rio, based on the object-oriented
programing paradigm (OOP), with an interactive graphical interface for modeling and an educational
approach. Four numerical solvers for obtaining the dynamic structural response were implemented.
The system of differential equations of motion may be analyzed on its coupled form, where free and
forced vibration are computed numerically, or on an uncoupled fashion, on the modal domain. On the
second case, it is possible to obtain analytical solutions for free vibration. The vibration modes are
found with the solution of the eigenvalue problem of an undamped oscillation system, achieved with a
Matlab built-in function. Viscous damping is treated as proportional to mass and to stiffness.
Consistent mass matrices were formulated for Euler-Bernoulli and Timoshenko beam bending
behavior theories, using parameters that unify both approaches. Alternatively, lumped mass matrices
were implemented as well. An effort in computer graphics was made to obtain multiple result
visualization options. A new interactive dialog of the graphical user interface was created in order to
display results on time and frequency domain, for each degree-of-freedom, being also possible to
visualize phase portraits of the solution. In addition, animations to depict the dynamic behavior of the
model were achieved.